Factors can be defined as numbers which can divide a parent number completely without leaving any remainder. For instance, the factors of the number 9 are 1 and 3 [1 x 9 = 9, 3 x 3 = 9]. So let us begin discussing the most fundamental of questions “what are the factors of 216?” In this particular article we will identify all the factors of 216 and will also analyze, scrutinize, highlight the methods that are utilized to find out the factors of 216. Students can adopt the techniques mentioned below to analyze the factors of other numbers as well.

There are 2 methods of prime factorization. They are the division method and the factor tree method. Identify the Factors of 216 using any one of the two methods.

### Division Method

Follow the given steps to find out the factors of 216.

Divide the number 216 with the smallest prime number that divides the given number exactly without producing any decimal values.

216 ÷ 2 = 108

Further, divide the number 108 with the smallest prime number

108 ÷ 2 = 54

54 is further divided with the smallest prime number i.e. 2

54 ÷ 2 = 27

Divide 27 with the smallest prime number i.e. 3

27 ÷ 3 = 9

9 is further divided with the smallest prime number

9 ÷ 3 = 3

3 is further divided

3 ÷ 3 =1

1 cannot be further divided

Multiply all the prime numbers we have used for division. We have used 2 and 3 prime numbers. Both of them are used 3 times.

The prime factors of 216 are 2×2×2×3×3×3. They are written as 23 × 33.

Let us now analyze another method to answer the question of “what are the factors of 216?”

### Factor Tree Method

We can find the factors of 216 using the factor tree method. Follow the given steps.

Write the pair of factors of 216 and the branches of the tree.

The initial factor pairs of 216 are 2 and 108 (branches)

As 2 is a prime number, it cannot be factorized further. We can factorize 108.

Write the factor pairs of 108.

The initial factor pairs of 108 are 2 and 54.

Factorize 54 to get other factors of 216.

Factor pairs of 54 are 2 and 27.

27 is factored further. Factors of 27 are 3 x 3 x 3 which can be denoted as 33.

What are all the factors of 216? Writing all factors of 216 together, we get 2×2×2×3×3×3.

Here is the representation of the factor tree to find 216 prime factorization

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One can find the prime factorization of 216 using any one of the above steps.

A factor pair is a pair of numbers that on multiplication produce the given number. For any given number, we can have positive and negative factor pairs.

Note: The factors pairs are usually positive. No negative factor pairs are found generally.

The factor pairs of 216 are:

Positive Factor Pairs:

2 × 108.

3 × 54.

4 × 72.

6 × 36.

8 × 27.

9 × 24.

12 × 18.

On multiplying the above pairs of numbers, we get 216.

The positive factor pairs are (2, 108) (3, 54) (4, 72) (6, 36) (8, 27) (9, 24) (12, 18).

Negative Factor Pairs:

-2 × -108.

-3 × -54.

-4 × -72.

-6 × -36.

-8 × -27.

-9 × -24.

-12 × -18.

On multiplying the above pairs of numbers, we get 216.

The negative factor pairs are (-2, -108) (-3, -54) (-4, -72) (-6, -36) (-8, -27) (-9, -24) (-12, -18).

The total number of factor pairs of 216 is 14 out of which 7 are positive and 7 are negative.

Division method:

The first step involves dividing the number by the smallest prime number. Again, divide the resulting number with the smallest prime number. Repeat the process till you get the number that cannot be factored further.

Write down all the factors used in this division process. These are the factors of the given number.

Factor Tree Method:

In the factor tree method, identify the initial factor pair of the given number. These factor pairs are considered as branches of the factor tree.

Identify the factor pairs of the branches. Further sub-branches are produced.

Repeat the same process till you arrive at the number that is not factorized further.

Write the prime numbers together which are the factors for the given number.

By performing either of the two methods, factor pairs are obtained for the given number. These methods apply for small and large numbers like 120, 216, 524, 1028, 2024, 5000 etc.

FAQ (Frequently Asked Questions)

1. What is the difference between Prime numbers and Factors?

A prime number is a number greater than 1 and does not contain factors. The number is produced by multiplying the same number with 1. Prime numbers are not produced by the multiplication of any whole numbers. Taking an example of 13. The number can be obtained by multiplying 1 with itself. Hence, there are no such factors other than 1 and 13.

On the other hand, factors are the numbers that on multiplication give a new number. The factors of prime numbers are 1 and the number itself. Composite numbers have more than 2 factors. Taking the same example of 13. In this case, the factors are only 1 and the number itself 13.

2. What is the prime factorization of 216?

We have already addressed the difference between Prime number and Factors. Now, prime factorization is a set of prime numbers that are factors of a particular number or variable. In the case of the number 216, if you practically do it, one can understand that its prime factors are 2 and 3. To be exact, 2^{3} has a value of 8 and 3^{3} has a value of 27. Multiplying both the numbers with root in consideration, the prime factors will generate 216 in the end result. As the name suggests, prime factorizations will always have prime numbers as factors which need to be understood.